1. 02-June-2003 Aseem Talukdar Department of Physics University of Cincinnati Cincinnati-OH Fabrication of 2D electron System by MBE and QHE

2.  2 D electron System  MBE technique  QHE Outlines:

3. 2D electron System E n =(n+1/2) ħ  c + g    +  z  c =eB/ m*  nk (r)~  n (y+c p x /eB) e i(k x x+k z z) Density of States ::

4. Potential well of width d  ~  2 ħ 2 /(2md 2 ) for 2D behavior k B T <  d ~ 10 nm T~130 K E~100 meV d~ 2 nm

5. Examples::  MOS structure (MOSFET)  GaAs/Ga 1-x Al x As heterostructure

6. Molecular Beam Epitaxy::  Technique for growing semiconductor layered structure  Allows Controlled growth of semiconductor layers with monolayer precision.

7. MBE::  Schematic of MBE  Effusion Cells  CAR assembly  Cryopanels  RHEED Gun

8. Classical Hall Effect(1879) Lorentz Force Law :: R h =E y /(J x B)=V y d/(BI x ) R h – Hall Coefficient d - thickness (along Z-axis) Drude Picture :: R h =-1/(ne) =>Hall Resistance R xy =-E y /J x =R h B  B

9. QHE-Klaus von Klitzing (1980) Transverse resistance 

10. Conclusions:: MBE provides a convenient way to prepare 2D electron system Ability to control band gap and grow one layer of semiconductor material at a time results in the possibility of development of electronic and optoelectronic devices